bessels

Bessels

Illustrate spherical Bessel function of first kind with gnuplot.

Bessel functions are canonical solutions y(x) for Bessel differential equation.

Here algorithm implements Frobenius method.

Definition

Bessel differential equation expression :

Isolating terms

• Wikipedia
• Wolfram

Feature

Cache

• Factorial lower than 23 into table.
• Bessels function order from 0 to 6 into data matrix (200 values per order, step 0.1 means 0.0 upto 20.0).

Compile

gcc -g -ggdb3 -std=c17 -Wall -pedantic src/bessel.c -o ./bessel -lm

Run

Usage

./bessel -h

Csv output

./bessel -d1 > bessel.csv

Plot

Dependency

sudo apt install gnuplot

2D

./bessel -d2 > bessel2d.dat && gnuplot ./bessel2d.gnuplot

3D

./bessel -d3 > bessel3d.dat && gnuplot ./bessel3d.gnuplot

Use case

FM bandwidth calculation

Bessel function zeros are exploited in frequency modulated (FM) radio transmission.
FM transmission is mathematically represented by a harmonic distribution of a sine wave carrier
modulated by a sine wave signal which can be represented with Bessel Functions.
The carrier or sideband frequencies disappear when the modulation index
(the peak frequency deviation divided by the modulation frequency)
is equal to the zero crossing of the function for the nth sideband.

• How to Calculate Bandwidth Using Carson’s Rule & Bessel Function Table for Frequency Modulation

Solving the schrodinger equation in cylindrical well

• APPLICATION - SOLUTION TO SCHROEDINGER’S EQUATION IN A CYLINDRICAL WELL